Chapter 1: Algebra Review Flashcards
Commutative Property
numbers can be added/multiplied in any order.
Associative Property
numbers can be grouped in any way
Distributive Property
you have to multiply a number into parentheses
Property of Opposites
when you add opposite numbers you get 0 (-7+7)
Symmetric Property
when something flipped sides of the equal sign (2t=4 and 4=2t)
Transitive Property
when two items are equal to a third item, the two are equal (a=b b=c a=c)
What are the steps to solve combined inequalities?
- simplify each side
- get like terms on one side of the inequality
- get variable by itself
When do flip the inequality sign?
when you multiply or divide by a negative
When graphing use…
( )
When graphing or equal to use…
[ ]
Conjunction
a sentence formed by joining two statements with AND
only true when both statements are true
Disjunction
a sentence formed by joining two statements with OR
only true when one statement is true
Absolute Value
distance from a number and 0
Extraneous Solution
a solution derived from another solution that doesn’t fit the original equation
What are the steps to solve absolute value equations?
- isolate absolute value by itself
- determine if conjunction or disjunction
- setup two equations
- solve
How can you easily determine if a absolute value equations is a con/disjunction?
L”and” of G”or”
Less than is conjunction
Greater than/equal is disjunction
What is a constant?
quantity that is always the same
What is a variable quantity?
quantity that changes
What is the different between a numerical and algebraic expression
an algebraic expression has variables
What is an easy way to identify patterns
a table of inputs and outputs
What are rational numbers?
all numbers you can write with terminating or repeating decimals
What are irrational numbers?
all numbers without terminating and repeating decimals
What are whole numbers?
numbers that are neither negative nor fractions
What are integers?
number that are either positive or negative but not fractions
What is a term?
expression of a number and/or variable (ex. 12x)
What is a coefficient?
the numerical factor of a term (ex. 4 is coefficient of 4x)
What is an equation?
statement that two expressions are equal
